













| Model | (Single Digits) | (Multi Digits) | ||
|---|---|---|---|---|
| Train | Test | Train | Test | |
| baseline | ||||
| LTN | ||||
| Model | Number of training examples | |||
|---|---|---|---|---|
| (Single Digits) | (Multi Digits) | |||
| 30 000 | 3 000 | 15 000 | 1 500 | |
| baseline | ||||
| LTN | ||||
| DeepProbLog | ||||










| Task | Network | Architecture |
|---|---|---|
| 4.1 4.2 | MLP | Dense(16)*, Dense(16)*, Dense(1) |
| MLP | Dense | |
| Dense(8)*, Dropout(0.2), Dense(1) | ||
| 4.3 4.4 | MLP | |
| CNN | MNISTConv, Dense(84)*, Dense(10) | |
| baseline – SD | ||
| baseline – MD | MNISTConv | |
| 4.5 4.6 4.7 | MLP | Dense(8)*, Dense(8)*, Dense(1) |
| MLP | Dense(16)*, Dense(16)*, Dense(16)*, Dense(1) | |
| MLP_S | Dense(8)*, Dense(8)*, Dense(1) | |
| MLP_F | Dense(8)*, Dense(8)*, Dense(1) | |
| MLP_C | Dense(8)*, Dense(8)*, Dense(1) |
| Name | ||||
|---|---|---|---|---|
| Goedel | if | |||
| Goguen/Product | ||||
| Lukasiewicz |
| Name | S-Implication | R-Implication | |
|---|---|---|---|
| Kleene-Dienes | - | ||
| Goedel | |||
| Reichenbach | - | ||
| Goguen | - | ||
| Lukasiewicz |
| Commutativity of | |||||
| Associativity of | |||||
| Distributivity of | |||||
| Distributivity of | |||||
| Distrib. of | |||||
| Double negation | |||||
| Law of excluded middle | |||||
| Law of non contradiction | |||||
| De Morgan’s laws | |||||
| Material Implication | |||||
| Contraposition | |||||
| Single-Passing | Vanishing | Exploding | |
|---|---|---|---|
| Goedel (mininum) | |||
| Goguen (product) | |||
| Lukasiewicz | |||
| Single-Passing | Vanishing | Exploding | |
|---|---|---|---|